Summary: Equilibrium roughening transition in a one-dimensional modified sine-Gordon model
Saúl Ares*
Grupo Interdisciplinar de Sistemas Complejos (GISC) and Departamento de Matemáticas, Universidad Carlos III de Madrid,
Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
Angel Sánchez
Grupo Interdisciplinar de Sistemas Complejos (GISC) and Departamento de Matemáticas, Universidad Carlos III de Madrid,
Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, 50009 Zaragoza, Spain
(Received 10 June 2004; revised manuscript received 7 October 2004; published 27 December 2004)
We present a modified version of the one-dimensional sine-Gordon model that exhibits a thermodynamic,
roughening phase transition, in analogy with the two-dimensional usual sine-Gordon model. The model is
suited to study the crystalline growth over an impenetrable substrate and to describe the wetting transition of
a liquid that forms layers. We use the transfer integral technique to write down the pseudo-Schrödinger
equation for the model, which allows us to obtain some analytical insight, and to compute numerically the free
energy from the exact transfer operator. We compare the results with Monte Carlo simulations of the model,
finding a perfect agreement between both procedures. We thus establish that the model shows a phase transition
between a low-temperature flat phase with intriguing nontrivial properties and a high-temperature rough one.
The fact that the model is one-dimensional and that it has a true phase transition makes it an ideal framework
for further studies of roughening phase transitions.
DOI: 10.1103/PhysRevE.70.061607 PACS number(s): 81.15.Aa, 68.35.Ct, 68.35.Rh, 05.40. a